Projects:BrainConnectivity - Revision history

Pega85: /* Exploration of Functional Connectivity via Clustering */

2011-10-28T18:17:07Z

Exploration of Functional Connectivity via Clustering

Pega85: /* Robust Feature Selection in Functional Connectivity to Classify Schizophrenia Patients */

2011-10-28T18:14:56Z

Robust Feature Selection in Functional Connectivity to Classify Schizophrenia Patients

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:13:25Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:11:21Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:11:03Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:10:11Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:07:43Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:06:29Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:05:20Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

Pega85: /* Joint Modeling of Anatomical and Functional Connectivity for Population Studies */

2011-10-28T18:02:11Z

Joint Modeling of Anatomical and Functional Connectivity for Population Studies

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 We used data from 7 subjects with a diverse set of visual experiments including localizer, morphing, rest, internal tasks, and movie. The functional scans were pre-processed for motion artifacts, manually aligned into the Talairach coordinate system, detrended (removing linear trends in the baseline activation) and smoothed (8mm kernel).
-Fig. 5 shows the 2-system partition extracted in each subject independently of all others. It also displays the boundaries of the intrinsic system determined through the traditional seed selection, showing good agreement between the two partitions. Fig. 6 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.
+Fig. 6 shows the 2-system partition extracted in each subject independently of all others. It also displays the boundaries of the intrinsic system determined through the traditional seed selection, showing good agreement between the two partitions. Fig. 7 presents the results of further clustering the stimulus-driven cluster into two clusters independently for each subject.
 <table>
-<tr> <th> '''Fig 5. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 6. 3-System Parcelation. Results for all 7 subjects.'''
+<tr> <th> '''Fig 6. 2-System Parcelation. Results for all 7 subjects.''' <th> '''Fig 7. 3-System Parcelation. Results for all 7 subjects.'''
 <tr> <td align="center">
 [[Image:mit_fmri_clustering_parcellation2_shb1_4.png |400px]]
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 </table>
-Fig. 7 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 8 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 9, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.
+Fig. 8 presents the group average of the subject-specific 2-system maps. Color shading shows the proportion of subjects whose clustering agreed with the majority label. Fig. 9 shows the group average of a further parcelation of the intrinsic system, i.e., one of two clusters associated with the non-stimulus-driven regions. In order to present a validation of the method, we compare these results with the conventional scheme for detection of visually responsive areas. In Fig. 10, color shows the statistical parametric map while solid lines indicate the boundaries of the visual system obtained through clustering. The result illustrate the agreement between the two methods.
 <table>
-<tr><th> '''Fig 7. 2-System Parcellation. Group-wise result.''' <th> '''Fig 8. Validation: Parcelation of the intrinsic system.'''
+<tr><th> '''Fig 8. 2-System Parcellation. Group-wise result.''' <th> '''Fig 9. Validation: Parcelation of the intrinsic system.'''
 <tr> <td align="center">
 [[Image:mit_fmri_clustering_parcellation2_xsub.png |thumb|570px]]
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 {|
-|+ '''Fig 9. Validation: Visual system.'''
+|+ '''Fig 10. Validation: Visual system.'''
 |valign="top"|[[Image:mit_fmri_clustering_validation.png |thumb|1150px]]
 |}
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 <table>
-<tr> <th> '''Fig 10. Varying the number of Nystrom Samples''' <th> '''Fig 11. Nystrom consistency for 2,000 random samples'''
+<tr> <th> '''Fig 11. Varying the number of Nystrom Samples''' <th> '''Fig 12. Nystrom consistency for 2,000 random samples'''
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-Fig 10. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.
+Fig 11. depicts the median clustering difference when varying the number of Nystrom samples. Values represent the percentage of mismatched voxels w.r.t. the 4,000-sample template. Error bars delineate the <em>10th</em>-<em>90</em> percentile region. The median clustering difference is less than 1% for 1,000 or more Nystrom samples, and the <em>90th</em> percentile difference is less than 1% for 1,500 or more samples. This experiment suggests that Nystrom-based SC converges to a stable clustering pattern as the number of samples increases. Based on these results, we chose to use 2,000 Nystrom samples for the remainder of this work. At this sample size, less than 5% of the runs for 2,4,5 clusters and approximately 8% of the runs for 3 clusters differed by more than 5% from the 4,000-sample template.
-The box plot in Fig 11. summarizes the consistency of Nystrom-based Spectral Clustering across
+The box plot in Fig 12. summarizes the consistency of Nystrom-based Spectral Clustering across
 different random samplings. The red lines indicate median values, the box corresponds to the upper and lower quartiles, and error bars denote the <em>10th</em> and <em>90th</em> percentiles. Here, we perform SC 10 times on each participant using 2,000 Nystrom samples. We then align the cluster maps and compute the percentage of mismatched voxels between each unique pair of runs. This yields a total of 45 comparisons per participant. In all cases, the median clustering difference is less than 1%, and the <em>90th</em> percentile value is less than 2.1%. Empirically, we find that Nystrom SC predictably converges to a second or third cluster pattern in only a handful of participants. This experiment suggests that we can obtain consistent clusterings with only 2,000 Nystrom samples.
 <table>
-<tr> ''' Fig 12. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
+<tr> ''' Fig 13. Clustering results across participants. The brain is partitioned into 5 clusters using Spectral Clustering/K-Means, and various seed are selected for Seed-Based Analysis. The color indicates the proportion of participants for whom the voxel was included in the detected system.'''
 <tr> <th> '''Spectral Clustering''' <th> '''K-Means''' <th> '''Seed-Based'''
 <tr>
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 </table>
-Fig 12. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.
+Fig 13. shows clearly that both Spectral Clustering and K-Means can identify well-known structures such as the default network, the visual cortex, the motor cortex, and the dorsal attention system. Spectral Clustering and K-Means also identified white matter. In general, one would not attempt to delineate this region using seed-based correlation analysis because we regress out the white matter signal during the preprocessing. In our experiments Spectral Clustering and K-Means achieve similar clustering results across participants. Furthermore, both methods identify the same functional systems as seed-based analysis without requiring <em>a priori</em> knowledge about the brain and without significant computation. Thus, clustering algorithms offer a viable alternative to standard functional connectivity analysis techniques.

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 <table>
-<tr> '''Fig 2. Stability of the GI values and t-scores on a ''log'' scale. For visualization, the values are normalized by the maximum GI and maximum t-score, respectively. Thick lines represent mean values, and the error bars correspond to standard deviations over the 100 cross-validation runs.'''
+<tr> '''Fig 3. Stability of the GI values and t-scores on a ''log'' scale. For visualization, the values are normalized by the maximum GI and maximum t-score, respectively. Thick lines represent mean values, and the error bars correspond to standard deviations over the 100 cross-validation runs.'''
 <tr> <td align="center">
 [[Image:Abs_CompareVariation_XcorrLog_orig_DTI2.png |500px]]
 </table>
-Fig. 2 depicts the stability of GI values and t-scores for each functional correlation across all 100 cross-validation runs. As seen, the t-scores exhibit far greater variability that the Gini Importance values. Additionally, the variance in GI is concentrated among the top features, whereas less-informative features are always assigned values near zero. Hence, although the top functional correlations may be ranked differently during each cross-validation run, the Random Forest isolates a consistent set of predictive features. In contrast, the t-scores vary uniformly over all features, regardless of significance. Thus, the set of predictive features can vary drastically over cross-validation runs.
+Fig. 3 depicts the stability of GI values and t-scores for each functional correlation across all 100 cross-validation runs. As seen, the t-scores exhibit far greater variability that the Gini Importance values. Additionally, the variance in GI is concentrated among the top features, whereas less-informative features are always assigned values near zero. Hence, although the top functional correlations may be ranked differently during each cross-validation run, the Random Forest isolates a consistent set of predictive features. In contrast, the t-scores vary uniformly over all features, regardless of significance. Thus, the set of predictive features can vary drastically over cross-validation runs.
 <table>
-<tr> '''Fig 3. Proportion of the 100 cross-validation runs during which the feature is selected. The solid lines denote performance based on GI values for various ''K''. The dashed lines represent the corresponding metric using t-scores.'''
+<tr> '''Fig 4. Proportion of the 100 cross-validation runs during which the feature is selected. The solid lines denote performance based on GI values for various ''K''. The dashed lines represent the corresponding metric using t-scores.'''
 <tr> <td align="center">
 [[Image:SelectedProp_orig_DTI2.png |500px]]
 </table>
-Fig. 3 shows the proportion of cross-validation runs during which a particular functional correlation is ranked among the top ''K'' features, as measured by GI value or t-score. We observe that the decay in the proportion of iterations based on GI is relatively sharp from one to zero. Hence, if a feature is relevant for group discrimination, it tends to be ranked among the top; otherwise, it is almost always ignored. In contrast, feature selection based on t-scores is inconsistent and depends on the dataset. It is worth noting that ''none'' of the functional correlations are ranked in the top 500 by t-score for all 100 cross-validation iterations.
+Fig. 4 shows the proportion of cross-validation runs during which a particular functional correlation is ranked among the top ''K'' features, as measured by GI value or t-score. We observe that the decay in the proportion of iterations based on GI is relatively sharp from one to zero. Hence, if a feature is relevant for group discrimination, it tends to be ranked among the top; otherwise, it is almost always ignored. In contrast, feature selection based on t-scores is inconsistent and depends on the dataset. It is worth noting that ''none'' of the functional correlations are ranked in the top 500 by t-score for all 100 cross-validation iterations.
-'''Fig 4. Connections selected during at least half of the cross-validation runs. Blue lines indicate higher connectivity in the control group; yellow lines indicate higher connectivity in the schizophrenia population.'''
+'''Fig 5. Connections selected during at least half of the cross-validation runs. Blue lines indicate higher connectivity in the control group; yellow lines indicate higher connectivity in the schizophrenia population.'''
 <table>
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 </table>
-Fig. 4 depicts the connections selected during at least half of the cross-validation iterations. Table XX reports the classification accuracy. For GI, we depict results for K=15, which yields the best classification accuracy. For t-score, we use K=150, which roughly corresponds to p-values less than 0.05. As seen, the significant functional correlations are disjoint between the feature selection methods. From these results, we conclude that the Gini Importance is a more robust feature selection criterion for clinical data than the univariate t-test.
+Fig. 5 depicts the connections selected during at least half of the cross-validation iterations. Table XX reports the classification accuracy. For GI, we depict results for K=15, which yields the best classification accuracy. For t-score, we use K=150, which roughly corresponds to p-values less than 0.05. As seen, the significant functional correlations are disjoint between the feature selection methods. From these results, we conclude that the Gini Importance is a more robust feature selection criterion for clinical data than the univariate t-test.
 <table>

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 </table>
-Unlike voxel- and ROI-based analysis, we model the behavior of pairwise connections between regions of the brain. We define two latent variables: ''anatomical connectivity'' is a binary random variable that indicates the presence or absence of a direct anatomical pathway between the regions. ''Functional connectivity'' is a tri-state random variable that represent little or no functional co-activation, positive functional synchrony, and negative functional synchrony between the regions. Our observed variables are correlations in resting-state fMRI and average FA values along the white matter tracts. We model differences between the groups within the latent connectivities alone and share the data likelihood distributions between the two populations.
+Unlike voxel- and ROI-based analysis, we model the behavior of pairwise connections between regions of the brain. Fig. 1 depicts our generative model. We define two latent variables: ''anatomical connectivity'' is a binary random variable that indicates the presence or absence of a direct anatomical pathway between the regions. ''Functional connectivity'' is a tri-state random variable that represent little or no functional co-activation, positive functional synchrony, and negative functional synchrony between the regions. These variables specify templates for each (control, schizophrenia) population. Our observed variables are correlations in resting-state fMRI and average FA values along the white matter tracts. We model differences between the groups within the latent connectivities alone and share the data likelihood distributions between the two populations.
 ''' ''Experimental Results'' '''
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 We segmented the structural images into 77 anatomical regions with Freesurfer. To inject prior clinical knowledge, we pre-selected 8 brain structures (corresponding to 16 regions) that are believed to play a role in schizophrenia: the superior temporal gyrus, rostral middle frontal gyrus, hippocampus, amygdala, posterior cingulate, rostral anterior cingulate, parahippocampal gyrus, and transverse temporal gyrus. We model only the 1096 unique pairwise connections between these ROIs and all other regions in the brain.
-'''Fig 1. Significant anatomical and functional connectivity differences. Blue lines indicate higher connectivity in the control group; yellow lines indicate higher connectivity in the schizophrenia population.'''
+'''Fig 2. Significant anatomical and functional connectivity differences. Blue lines indicate higher connectivity in the control group; yellow lines indicate higher connectivity in the schizophrenia population.'''
 <table>
 <tr> <td align="center">
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 </table>
-Fig. 1 depicts the significantly different anatomical and functional connections identified by the algorithm.  As seen, schizophrenia patients exhibit increased functional connectivity between the parietal/posterior cingulate region and the frontal lobe and reduced functional connectivity between the parietal/posterior cingulate region and the temporal lobe. These results confirm the hypotheses of widespread functional connectivity changes in schizophrenia and of functional abnormalities involving the default network.
+Fig. 2 depicts the significantly different anatomical and functional connections identified by the algorithm.  As seen, schizophrenia patients exhibit increased functional connectivity between the parietal/posterior cingulate region and the frontal lobe and reduced functional connectivity between the parietal/posterior cingulate region and the temporal lobe. These results confirm the hypotheses of widespread functional connectivity changes in schizophrenia and of functional abnormalities involving the default network.
 The differences in anatomical connectivity implicate the superior temporal gyrus and hippocampus. We note that relatively few anatomical connections exhibit significant differences between the two populations. This may stem from our choice of ROIs. In particular, we rely on Freesurfer parcellations, which provide anatomically meaningful correspondences across subjects and mitigate the effects of minor registration errors. However, they may be too big to capture structural differences between the groups. We emphasize that our model can be easily applied to finer scale parcelations in future studies.

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 '''Fig 1. Joint model for the effects of schizophrenia. The pairwise connections are indexed with ''n=1,...,N''.  ''A_n'' represents the latent anatomical connectivity of the ''nth'' connection in the control template, and ''F_n'' denotes the corresponding latent functional connectivity. ''D_nj'' and ''B_nj'' are the observed DWI and fMRI measurements, respectively, for the ''nth'' connection in the ''jth'' subject in the control population. The schizophrenia templates are identified by an overbar, and the subjects are indexed by ''m=1,\ldots,M''. Squares indicate non-random parameters; circles indicate random variables; observed variables are shaded.'''
 <table>
 <tr> <td align="center">
 [[Image:GenModel3_not.png]]

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 The interaction between functional and anatomical connectivity provides a rich framework for understanding the brain. Functional connectivity is commonly measured via temporal correlations in resting-state fMRI data. These correlations are believed to reflect the intrinsic functional organization of the brain. Anatomical connectivity is often measured using DWI tractography, which estimates the configuration of underlying white matter fibers. In this work we propose and demonstrate a novel probabilistic framework to infer the relationship between these modalities. The model is based on ''latent'' connectivities between brain regions and makes intuitive assumptions about the data generation process. We present a natural extension of the model to population studies, which we use to identify widespread connectivity changes in schizophrenia.
 <table>
 <tr> <td align="center"> '''Fig 1. Joint model for the effects of schizophrenia. The pairwise connections are indexed with ''n=1,...,N''.  ''A_n'' represents the latent anatomical connectivity of the ''nth'' connection in the control template, and ''F_n'' denotes the corresponding latent functional connectivity. ''D_nj'' and ''B_nj'' are the observed DWI and fMRI measurements, respectively, for the ''nth'' connection in the ''jth'' subject in the control population. The schizophrenia templates are identified by an overbar, and the subjects are indexed by ''m=1,\ldots,M''. Squares indicate non-random parameters; circles indicate random variables; observed variables are shaded.'''

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 <table>
-<tr> <td align="center"> '''Fig 1. Joint model for the effects of schizophrenia. The pairwise connections are indexed with <math>n=1</math>.'''
+<tr> <td align="center"> '''Fig 1. Joint model for the effects of schizophrenia. The pairwise connections are indexed with ''n=1,...,N''.'''
 <tr> <td align="center">
 [[Image:GenModel3_not.png]]